Light intensity notes

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Introduction

Sam Davyson PHY//12// 19/09/05

Mr Ford – Chapter 12 – Revision Notes

Light Intensity

In space the light intensity from distant stars can be used to approximate the distances between the stars and us. This idea can be mimicked in the laboratory with a light box, a lux meter and a measuring rule. Taking measurements and plotting them reveals a linear relationship between light intensity and the reciprocal of the distance squared. It turns out that they are in fact proportional to one another.

There are some obvious problems with this technique:

Don’t know how bright the stars really are.

We must assume that the intensity is not affected by different mediums (including the atmosphere).

Measuring Distance using Parallax

Parallax is a technique that uses trigonometry and the difference between the apparent positions (referring to the “fixed” background stars) of a distant object from two different points along a base line. The longer the base line the further you can see. On earth the best we can do is looking at the object twice with 6 months between each viewing. This gives a baseline of 2Au = 300 Million km.

-1, and change in tback and change in tout are time between getting two pulses back and time between sending two pulses respectively.

The Doppler Shift

λout and λback are fairly self explanatory, and obviously λback > λout if the object is moving away, and the opposite if it is not. This differs from the method used with the asteroid as continuous waves rather than pulses are used. The formula that is used is not very different to the previous one though:

and if v << c (much less) then . The speciality of being able to use continuous waves rather than pulses is important when a one-way measuring method is used. In this the object is too far away to send a pulse to, however the object is emitting EM radiation. The change in wavelength of this radiation as it moves through space can be used to determine the relative velocity of the object. As this is one-way measuring the formula is modified (no need to account for both ways) to: . To determine the black lines in the emission spectrum that are absorbed by abundant elements in space (H and He)

Δλ > 0 indicates that the distances between every pair of objects is increasing (except locally where gravity can cause the reverse effect) and that the universe is expanding. This points to everything (once upon a time) being at the same place. Making this evidence for the Big Bang theory.

Cosmic Microwave Background Radiation

As time has passed since the Big Bang the background radiation from the Big Bang has been cosmologically red-shifted by the expansion of the universe. Initially high energy photons were exchanged between particles but by 300 000 yrs after the bang, the λ was stretched to 1μm and the temperature had been reduced to 3000 K. This temperature fall is observed because as λ gets longer, f gets lower, so by E = hf, E gets lower, and E ∝ T giving a temperature fall. Today (14 Gyr later) the λ is 1mm (microwaves) and T = 2.7 K. This is also considered to be evidence for the Big Bang.

Ulber`s Paradox

This is a thought-experiment that suggests that if the Universe is infinite then everywhere you looked in the sky your line of sight would (eventually) end with a star, giving a white sky. Ulber found that the sky was black rather than white. He claimed that there were not enough stars for an infinite Universe, so it must be finite.

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